Applications of polynomial systems
 Responsibility
 David A. Cox ; with contributions by Carlos D'Andrea, Alicia Dickenstein, Jonathan Hauenstein, Hal Schenck, Jessica Sidman
 Publication
 Providence, Rhode Island : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, [2020]
 Physical description
 ix, 250 pages : illustrations (some color) ; 26 cm
 Series
 Regional conference series in mathematics ; no. 134.
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Call number  Status 

QA1 .R33 NO.134  Unknown 
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Description
Creators/Contributors
 Author/Creator
 Cox, David A., author.
 Contributor
 D'Andrea, Carlos (Carlos Antonio), 1973 author.
 Dickenstein, Alicia, author.
 Hauenstein, Jonathan D., author.
 Schenck, Henry K., 1963 author.
 Sidman, Jessica, author.
 Conference Board of the Mathematical Sciences, issuing body.
 National Science Foundation (U.S.), sponsoring body.
 NSFCBMS Regional Conference in the Mathematical Sciences (2018 : Fort Worth, Tex.)
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 225241) and index
 Contents

 Elimination theory Numerical algebraic geometry Geometric modeling Rigidity theory Chemical reaction networks Illustration credits Bibliography Index.
 (source: Nielsen Book Data)
 Summary

Systems of polynomial equations can be used to model an astonishing variety of phenomena. This book explores the geometry and algebra of such systems and includes numerous applications. The book begins with elimination theory from Newton to the twentyfirst century and then discusses the interaction between algebraic geometry and numerical computations, a subject now called numerical algebraic geometry. The final three chapters discuss applications to geometric modeling, rigidity theory, and chemical reaction networks in detail. Each chapter ends with a section written by a leading expert. Examples in the book include oil wells, HIV infection, phylogenetic models, fourbar mechanisms, border rank, font design, StewartGough platforms, rigidity of edge graphs, Gaussian graphical models, geometric constraint systems, and enzymatic cascades. The reader will encounter geometric objects such as Bezier patches, CayleyMenger varieties, and toric varieties; and algebraic objects such as resultants, Rees algebras, approximation complexes, matroids, and toric ideals. Two important subthemes that appear in multiple chapters are toric varieties and algebraic statistics. The book also discusses the history of elimination theory, including its near elimination in the middle of the twentieth century. The main goal is to inspire the reader to learn about the topics covered in the book. With this in mind, the book has an extensive bibliography containing over 350 books and papers.
(source: Nielsen Book Data)
Subjects
 Subject
 Polynomials > Congresses.
 Commutative algebra > Congresses.
 Geometry, Algebraic > Congresses.
 Commutative algebra.
 Geometry, Algebraic.
 Polynomials.
 Commutative algebra  Computational aspects and applications [See also 14Qxx, 68W30]  Solving polynomial systems; resultants.
 Algebraic geometry  Computational aspects in algebraic geometry [See also 12Y05, 13Pxx, 68W30]  None of the above, but in this section.
 Commutative algebra  Computational aspects and applications [See also 14Qxx, 68W30]  Applications of commutative algebra (e.g., to statistics, control theory, optimization, etc.)
 Algebraic geometry  Special varieties  Toric varieties, Newton polyhedra [See also 52B20].
 Convex and discrete geometry  Discrete geometry  Rigidity and flexibility of structures [See also 70B15].
 Statistics  Multivariate analysis [See also 60Exx]  None of the above, but in this section.
 Numerical analysis  Nonlinear algebraic or transcendental equations  Global methods, including homotopy approaches [See also 58C30, 90C30].
 Computer science {For papers involving machine computations and programs in a specific mathematical area, see Section04 in that area}  Computing methodologies and applications  Computeraided de.
 Biology and other natural sciences  Physiological, cellular and medical topics  Systems biology, networks.
Bibliographic information
 Publication date
 2020
 Series
 Conference Board of the Mathematical Sciences CBMS regional conference series in mathematics, 01607642 ; number 134
 Note
 "With support from the National Science Foundation."
 "The five chapters are based on the NSFCBMS Regional Research Conference Applications of Polynomial Systems held at Texas Christian University June 48, 2018."
 ISBN
 9781470451370 paperback
 1470451379 paperback
 9781470455897 electronic book